CALCULATE THE RMS VELOCITY OF METHANE AT 298 KELVIN.
u(rms) = sqrt(3RT/M)
Substitute 8.314 for R, 298 for T, and molar mass for M). Solve.
To calculate the root mean square (RMS) velocity of methane at 298 Kelvin, you can use the following formula:
RMS Velocity = √((3 * R * T) / M)
Where:
- RMS Velocity is the root mean square velocity.
- R is the gas constant, which is 8.314 J/(mol·K).
- T is the temperature in Kelvin.
- M is the molar mass of methane, which is 16.04 g/mol.
Let's substitute the values into the formula and calculate the RMS velocity:
RMS Velocity = √((3 * 8.314 J/(mol·K) * 298 K) / 16.04 g/mol)
First, let's convert the molar mass of methane from grams to kilograms:
M = 16.04 g/mol = 0.01604 kg/mol
Now, let's substitute the values:
RMS Velocity = √((3 * 8.314 J/(mol·K) * 298 K) / 0.01604 kg/mol)
Simplifying the equation:
RMS Velocity = √((3 * 8.314 J/(mol·K) * 298 K) / 0.01604 kg/mol)
RMS Velocity ≈ √(6.235 J/mol)
Calculating the square root:
RMS Velocity ≈ 2.496 m/s
Therefore, the RMS velocity of methane at 298 Kelvin is approximately 2.496 m/s.